NONPARAMETRIC REGRESSION FUNCTION ESTIMATION BASED ON CENSORED DATA

Let （X₁, Y₁）, …, （X_n, Y_n） be i.i.d. R^d×R¹ random vectoos, E|Y|＜+∞. then m（x）=E（Y|x） is called a regression function, Now, T₁, …, T_n be i.i.d. samples of random variable T, independent of （X_i, Y_i）_i=1ⁿ. Set F（x,y）=P（X≥x,Y≥y）, G（t）=P（T≥t）, both F and G are unknown continuous survival functions. Based on obserations Z_i=min（X_i, Y_i） and δ_i=X_i≤Y_i only, we proposed an estimate m_n（x） of m（x）. Under some conditions it is shown that m_n（x）→m（x）, a. s. （n→+∞）.